Browsing by Author "Luc, Nguyen Hoang"

Now showing 1 - 11 of 11

Citation Count: Long, Le Dinh...et al. (2021). "An inverse source problem for pseudo-parabolic equation with Caputo derivative", Journal of Applied Mathematics and Computing.
An inverse source problem for pseudo-parabolic equation with Caputo derivative
(2021) Long, Le Dinh; Luc, Nguyen Hoang; Tatar, Salih; Baleanu, Dumitru; Can, Nguyen Huu; 56389
In this paper, we consider an inverse source problem for a fractional pseudo-parabolic equation. We show that the problem is severely ill-posed (in the sense of Hadamard) and the Tikhonov regularization method is proposed to solve the problem. In addition, we present numerical examples to illustrate applicability and accuracy of the proposed method to some extent.
Citation Count: Binh, Tran Thanh...et al. (2019). "Determination of source term for the fractional Rayleigh-Stokes equation with random data", Journal of Inequalities and Applications, Vol. 2019, No. 1.
Determination of source term for the fractional Rayleigh-Stokes equation with random data
(2019) Binh, Tran Thanh; Baleanu, Dumitru; Luc, Nguyen Hoang; Can, Nguyen-H; 56389
In this article, we consider the problem of finding a source term of a Rayleigh-Stokes equation. Our problem is not well-posed in the sense of Hadamard. The sought solution does not depend continuously on the given data. Using the truncation method and some new techniques on trigonometric estimators, we give the regularized solution. Moreover, the mean square error and convergence rates are established.
Citation Count: Luc, Nguyen Hoang...et al. (2021). "Identifying the initial condition for space-fractional sobolev equation", Journal of Applied Analysis and Computation, Vol. 11, No. 5, pp. 2402-2422.
Identifying the initial condition for space-fractional sobolev equation
(2021) Luc, Nguyen Hoang; Long, Le Dinh; Hang, Le Thi Diem; Baleanu, Dumitru; Can, Nguyen Hu; 56389
In this work, a final value problem for a fractional pseudo-parabolic equation is considered. Firstly, we present the regularity of solution. Secondly, we show that this problem is ill-posed in Hadamard’s sense. After that we use the quasi–boundary value regularization method to solve this problem. To show that the proposed theoretical results are appropriate, we present an illustrative numerical example. © 2021, Wilmington Scientific Publisher. All rights reserved.
Citation Count: Luc, Nguyen Hoang...et al. (2021). "Identifying the source function for time fractional diffusion with non-local in time conditions", Computational and Applied Mathematics, Vol. 40, No. 5.
Identifying the source function for time fractional diffusion with non-local in time conditions
(2021) Luc, Nguyen Hoang; Baleanu, Dumitru; Agarwal, Ravi P.; Long, Le Dinh; 56389
The diffusion equation has many applications in fields such as physics, environment, and fluid mechanics. In this paper, we consider the problem of identifying an unknown source for a time-fractional diffusion equation in a general bounded domain from the nonlocal integral condition. The problem is non-well-posed in the sense of Hadamard, i.e, if the problem has only one solution, the solution will not depend continuously on the input data. To get a stable solution and approximation, we need to offer the regularization methods. The first contribution to the paper is to provide a regularized solution using the modified fractional Landweber method. Two choices are proposed including a priori and a posteriori parameter choice rules, to estimate the convergence rate of the regularized methods. The second new contribution is to use truncation to give an estimate of Lp for the convergence rate. © 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.
Citation Count: Luc, Nguyen Hoang...et al. (2020). "Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator", Advances in Difference Equations, Vol. 2020, No. 1.
Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator
(2020) Luc, Nguyen Hoang; Huynh, Le Nhat; Baleanu, Dumitru; Can, Nguyen Huu; 56389
In this paper, we consider an inverse problem of identifying the source term for a generalization of the time-fractional diffusion equation, where regularized hyper-Bessel operator is used instead of the time derivative. First, we investigate the existence of our source term; the conditional stability for the inverse source problem is also investigated. Then, we show that the backward problem is ill-posed; the fractional Landweber method and the fractional Tikhonov method are used to deal with this inverse problem, and the regularized solution is also obtained. We present convergence rates for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. Finally, we present a numerical example to illustrate the proposed method.
Citation Count: Can, Nguyen Huu...et al. (2020). "Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel", Advances in Difference Equations, Vol. 2020, No.1.
Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel
(2020) Can, Nguyen Huu; Luc, Nguyen Hoang; Baleanu, Dumitru; Zhou, Yong; Long, Le Dinh; 56389
In this work, we study the problem to identify an unknown source term for the Atangana-Baleanu fractional derivative. In general, the problem is severely ill-posed in the sense of Hadamard. We have applied the generalized Tikhonov method to regularize the instable solution of the problem. In the theoretical result, we show the error estimate between the regularized and exact solutions with a priori parameter choice rules. We present a numerical example to illustrate the theoretical result. According to this example, we show that the proposed regularization method is converged.
Citation Count: Nam, Danh Hua Quoc...et al. (2020). "On a Kirchhoff diffusion equation with integral condition", Advances in Difference Equations, Vol. 2020, No. 1.
On a Kirchhoff diffusion equation with integral condition
(2020) Nam, Danh Hua Quoc; Baleanu, Dumitru; Luc, Nguyen Hoang; Can, Nguyen Huu; 56389
This paper is devoted to Kirchhoff-type parabolic problem with nonlocal integral condition. Our problem has many applications in modeling physical and biological phenomena. The first part of our paper concerns the local existence of the mild solution in Hilbert scales. Our results can be studied into two cases: homogeneous case and inhomogeneous case. In order to overcome difficulties, we applied Banach fixed point theorem and some new techniques on Sobolev spaces. The second part of the paper is to derive the ill-posedness of the mild solution in the sense of Hadamard.
Citation Count: Karapınar, Erdal...et al. (2021). "On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems", Advances in Difference Equations, Vol. 2021, No. 1.
On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems
(2021) Karapınar, Erdal; Binh, Ho Duy; Luc, Nguyen Hoang; Can, Nguyen Huu; 19184
In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order. Moreover, we present an example to illustrate the theory.
Citation Count: Luc, Nguyen Hoang...et al. (2020). "Reconstructing the right-hand side of a fractional subdiffusion equation from the final data", Journal of Inequalities and Applications, Vol. 2020, No. 1.
Reconstructing the right-hand side of a fractional subdiffusion equation from the final data
(2020) Luc, Nguyen Hoang; Baleanu, Dumitru; Long, Le Dinh; Can, Nguyen-Huu; 56389
In this study, we study an inverse source problem for the time-fractional diffusion equation, where the final data t=Tare given. We show that our problem is ill-posed in the sense of Hadamard. Applying a truncation method, we give the regularized solution. Finally, convergence estimates under a priori and a posteriori parameter choice rules are proved.
Citation Count: Huynh, Le Nhat...et al. (2021). "Recovering the space source term for the fractional-diffusion equation with Caputo–Fabrizio derivative", Journal of Inequalities and Applications, Vol. 2021, No. 1.
Recovering the space source term for the fractional-diffusion equation with Caputo–Fabrizio derivative
(2021) Huynh, Le Nhat; Luc, Nguyen Hoang; Baleanu, Dumitru; Long, Le Dinh; 56389
This article is devoted to the study of the source function for the Caputo–Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel. Here, we investigate the existence of the source term. Through an example, we show that this problem is ill-posed (in the sense of Hadamard), and the fractional Landweber method and the modified quasi-boundary value method are used to deal with this inverse problem and the regularized solution is also obtained. The convergence estimates are addressed for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. In addition, we give a numerical example to illustrate the proposed method.
Citation Count: Nguyen Duc Phuong; Nguyen Huy Tuan...et al. (2019). "Regularized solution for nonlinear elliptic equations with random discrete data", Mathematical Methods in the Applied Sciences, Vol. 42, No. 18, pp. 6829-6848.
Regularized solution for nonlinear elliptic equations with random discrete data
(Wiley, 2019) Phuong, Nguyen Duc; Tuan, Nguyen Huy; Baleanu, Dumitru; Luc, Nguyen Hoang; 56389
The aim of this paper is to study the Cauchy problem of determining a solution of nonlinear elliptic equations with random discrete data. A study showing that this problem is severely ill posed in the sense of Hadamard, ie, the solution does not depend continuously on the initial data. It is therefore necessary to regularize the in-stable solution of the problem. First, we use the trigonometric of nonparametric regression associated with the truncation method in order to offer the regularized solution. Then, under some presumption on the true solution, we give errors estimates and convergence rate in L-2-norm. A numerical example is also constructed to illustrate the main results.